Smoke+fire wispy and transparent in render, but fine in render preview
Unfortunately, (as mentioned in the linked thread), this issue is a bug.

There is a workaround however, which isn't ideal or 100% polished, but its a quick and dirty method to get the job done.

1. As you can see in the screenshot, I have the same issue (Note: This bug only applies to the 'Fire' flow type, the 'Fire &amp; Smoke' type renders without issues).



2. Begin by ensuring that Transparent is checked under Film in the Render Properties Panel, and also that the PNG Type is set to RGBA in Output.



3. Next add a large plane behind the fire object. Ensure that it is wider than the bounds of the camera and is far enough back from the fire object as not to cast light onto it. Give it a simple deep blue emission shader, with strength set to 1. (Note: I've noticed a bug here in 2.74 whereby if there is an object behind the viewport display of the smoke and fire, it wont dispay properly. Don't worry though, this doesn't seem to affect the renders.)



4. Render the image and jump on into the Compositing Screen Layout. Check the Use Nodes, Free Unused, and Backdrop boxes below the Node Editor, and add in a Viewer node.



5. Hit Shift+A and go Matte>Keying, add this to the Node tree.




6. In the Key Colour setting, use the Eye Dropper tool to sample the blue from the original render, this will mask out all hues from the render which display the selected colour. If the blue appears black, it's likely that you don't have the Use Alpha check-box ticked on the Viewer and Composite nodes.



7. This should update the render automatically in the bottom left Image Editor. If it has simply hover over the transparent render and hit F3. If not just give it another render, ensuring that the Compositing check-box is ticked under the Post Processing tab in the Render Properties Panel, and it should display the composite fine.



Et Voila, the final render! :) As I mentioned it's not a perfect solution, and where the blue was subtracted from the edge of the flame it has become slightly pink tinted, but for all intensive purposes it works okay, and colour correction could be applied either in Blender or in Photoshop/Gimp. Finger's crossed the bugs'll be fixed in the next release.